1. **State the problem:** We need to find the slope of the line passing through the points $(-3, -2)$ and $(2, 4)$. 2. **Recall the formula for slope:** The slope $m$ of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ This formula represents the vertical change (rise) over the horizontal change (run) between the two points. 3. **Substitute the given points:** Here, $x_1 = -3$, $y_1 = -2$, $x_2 = 2$, and $y_2 = 4$. So, $$m = \frac{4 - (-2)}{2 - (-3)}$$ 4. **Simplify the numerator and denominator:** $$m = \frac{4 + 2}{2 + 3} = \frac{6}{5}$$ 5. **Final answer:** The slope of the line is $$m = \frac{6}{5}$$ This means for every 5 units moved horizontally to the right, the line rises 6 units vertically.